1. Field of the Invention
The invention generally relates to the mechanical properties, material quality, mechanical behavior and bonding strength of carbon nanotoube and carbon nanofiber-based materials. More specifically, the invention relates to structures for thermal management of integrated circuit (IC) devices.
2. Discussion of the Prior Art
Since their discovery, carbon nanotubes (CNTs) and carbon nanofibers (CNFs) have attracted interest of a significant number of researchers and engineers. CNTs possess unique structure, as well as extraordinary mechanical, electrical, and optical properties. There are also numerous patents and patent applications that have been issued or filed in the area in question. It has been shown that CNTs can be used as optoelectronic devices, field effect transistors (FET), and sensors. It has also been found that thermal conductivity of CNTs can be exceptionally high: even higher than that of a diamond. Numerous studies, primarily theoretical, have been recently conducted to evaluate the thermal performance of CNTs and their applicability for heat removal in integrated circuits (IC). The thermal conductivity of single wall carbon nanotubes (SWCNT) was investigated using various simulation techniques, such as molecular dynamics (MD) simulation, non-equilibrium simulation, and the force field theory. Although the obtained data are inconsistent and show significant discrepancy, the data nonetheless confirmed that the expected level of CNT thermal conductivity could be quite high: 6,000 W/m·K, 375 W/m·K, 1,600 W/m·K, and 2,980 W/m·K, i.e. much higher than that of most of existing materials. There exists, therefore, significant interest in using CNTs as thermal interface materials (TIMs) for thermal management of ICs, and there exists a significant incentive in using CNTs and CNFs as TIMs.
As for the experimental studies, it has been found that the thermal conductivity of individual multiwall carbon nanotubes (MWCNT) at room temperature could be as high as 3,000 W/m·K. This result is within the region of theoretical predictions. For SWCNT dense-packed ropes, however, a rather low value of 35 W/m·K was obtained for mat samples. A thermal conductivity level of 150 W/m·K was reported by Shi et al for SWCNTs in a bundle, and having an average diameter of 10 nm. Theoretically, the thermal conductivity of MWCNTs should be lower when compared to SWCNTs. Indeed, some experiments showed that the thermal conductivity of aligned MWCNTs could be as low as 12-17 W/m·K. A somewhat higher value of 27 W/m·K was obtained by several other groups.
In general, research do date indicates that, although the thermal conductivity of CNT bundles could be significantly lower than the theoretical predictions (1,600-6,600 W/m K) and the conductivity of single CNTs there is, nonetheless, a clear indication that CNTs can have a higher conductivity than the regular TIMs that are currently used for IC cooling, which is only about 3-7 W/m·K. With all this information available, one can conclude that, although there is both a considerable interest in the use of CNTs and CNFs as TIMs and a significant incentive for doing that, there is still a long way to go until these devices are developed to an extent that they could become products, i.e. where they are commercially attractive, functionally and mechanically reliable, and environmentally durable.
It is clear also that, to come up with a feasible device, one should be able to develop a viable and a reliable product. To do that, one should know the major mechanical/physical characteristics of the CNT/CNF material.
Young's modulus (YM) is an important material characteristic of the CNT and CNF material, and therefore substantial effort is dedicated to its evaluation. The YM of CNTs, such as those shown with respect of FIG. 1, was measured by generating a thermal vibration of CNTs and using high resolution tunneling electron microscope (HRTEM). The mechanical behavior of individual CNFs was investigated using the nanoprobe manipulation method shown, for example, with respect to FIG. 2. It has been found that the YM of a CNT/CNF might depend on its diameter and, based on reported data, might change from 2 TPa to 200 GPa, when the CNT diameter changes from 5 nm to 40 nm. This information agrees with the experimental data that were obtained using the external oscillated electrical field assisted HRTEM. It has been found that the YM of the CNTs decreases exponentially with an increase in the CNT diameter. Carbon nanofibers (CNFs) produced by PECVD are characterized by much larger diameters (about 100 nm). Because of that, and also because of the far-from-ideal bamboo-like morphology of the CNFs, their effective Young's modulus (EYM) is expected to be much lower than that of the CNTs.
In this connection, it should be emphasized that there is a significant incentive in evaluating the effective Young's modulus (EYM) of the CNT/CNF array. The EYM characterizes, in a phenomenological fashion, the mechanical behavior of a CNT/CNF array treated as a, sort of, continuous material layer. The EYM might be quite different from the actual, micro- or nano-scale YM that could be found based on the testing of an individual CNT or a CNF. At the same time it might, and typically is, sufficient to have the most accurate information of the EYM to carry out a practical design of a CNT/CNF-based TIM. Therefore, in this disclosure the inventors herein treat the CNF array (CNFA) brush as a continuous elastic strip. The elastic response of a continuous, homogeneous, and isotropic elastic medium depends on two constants i.e. YM and Poisson's ratio, or on the two Lame constants, which are derivative of the above two constants. While the Poisson's ratio changes in relatively narrow limits, the YM and the EYM might be quite different for CNT/CNF materials obtained by using different synthesis methods. At the same time it is well known that it is the YM, and not the Poisson's ratio (unless the material exhibits very unusual mechanical behavior), that plays the most important role in the mechanical behavior and performance of materials.
Although many phenomena of the CNT/CNF materials behavior can be adequately described and explained only on the basis of quantum mechanics, it is often assumed that theory-of-elasticity, and even engineering mechanics methods, can be successfully employed to evaluate the YM of the CNT/CNF materials. There is an obvious incentive for the development of a practical methodology for the evaluation of the EYM of vertically aligned PECVD-synthesized CNFA and CNTA. In this disclosure, the inventors herein show how this could be done on the basis of the measured compressive-force vs. axial-displacement in the post-buckling mode.
There are several reasons why the axial displacements should be large enough to ensure that the CNFA behaves in the post-buckling mode conditions. First, the force-displacement relationships in the post-buckling mode can be obtained in a wide range of measured forces and displacements. Second, exact solutions exist (Euler's elastica) for the evaluation of the highly geometrically nonlinear bending deformations of flexible rods (beams). By treating CNFs as nonlinear beams/wires, one can use elasticasolutions to predict the EYM from the experimentally obtained force-displacement relationship. If the material exhibits nonlinear stress-strain relationship, i.e. if the EYM is stress dependent, then this dependency could be obtained as a suitable correction to the YM value obtained on the basis of the elastica solution. Finally, it is important that the interfacial pressure does not change significantly with the change in the axial displacements of the CNFA. This indeed takes place when the compressed CNFA is operated in the post-buckling condition. Because CNFs are intended to perform in the post-buckling modes in many practical applications, the evaluation of their behavior in such a mode enables one to obtain valuable information for these structural elements under in-use conditions.
The ability to evaluate the bonding, i.e. adhesive, strength of the CNT/CNF array to its substrate is another important problem in making a CNT/CNF-based TIM device into a commercial product. Satisfactory adhesion of the CNF array (CNFA) to its substrate is critical for making the CNF-based technology practical. Accordingly, there is an incentive for the development of an easy-to-use and effective method for the evaluation of such an adhesion. The adhesion strength of a single CNF to its substrate was addressed qualitatively, apparently for the first time, by Cui et al and by Chen et al. This was done in connection with the use of PECVD synthesized CNFs as probe tips in the atomic force microscopy imaging equipment. In the experiments described by these investigators, individual CNFs were directly grown on tipless cantilevers. In the reported observation, the CNF-probe was operated on a continuous scan mode for eight hours. No degradation in image resolution was observed. The CNFA is disclosed herein consists of billions of CNFs. The obtained information characterizes the performance of an ensemble of a plurality of CNFs. To translate the obtained experimental data into corresponding shearing stresses, one has to develop an analytical stress model that enables one to calculate the magnitude and the distribution of the interfacial shearing stress from the measured given, i.e. given, external force. In addition there is a need for designing a special test vehicle for the evaluation of the shearing off strength of the CNT/CNF structures in question. In the invention disclosed herein, the inventors teach how the maximum effective shear stress-at-failure for a CNFA fabricated on a thick Cu substrate could be determined and, if necessary, specified. As in the case of the Young's modulus, the inventors herein both use the term “effective” to emphasize that a plurality of CNFs and treat the CNFA “brush” as a sort of a continuous bonding layer. This approach enables one to use an analytical stress model that was developed for the evaluation of the interfacial shearing stress in an assembly with a continuous bonding layer. The developed model is a modification of the models that were suggested earlier for the evaluation of the interfacial thermally induced stresses in thermally mismatched assemblies